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The observed clustering of galaxies is expected to evolve with time, as structure continues to grow due to gravity. The exact evolution depends on cosmological parameters such as Lambda and Omegamatter. Larger values of Lambda, for example, lead to larger voids and higher density contrasts between overdense and underdense regions. By measuring the clustering of galaxies at higher redshift, one can break degeneracies that exist between the galaxy bias and cosmological parameters that are constrained by low redshift clustering measurements. It is therefore useful to determine the clustering of galaxies as a function of cosmic epoch, not only to further constrain cosmological parameters but also galaxy evolution.

One might expect the galaxy clustering amplitude r0 to increase over time, as overdense regions become more overdense as galaxies move towards groups and clusters due to gravity. However, the exact evolution of the clustering of galaxies depends not only on gravity, but also on the expansion history of the Universe and therefore cosmological parameters such as Lambda. Additionally, over time new galaxies form while existing galaxies grow in both mass and luminosity. Therefore, the expected changes of galaxy clustering as a function of redshift depend both on relatively well-known cosmological parameters and more unknown galaxy formation and evolution physics which likely depends on gas accretion, star formation, and feedback processes, as well as mergers.

For a given cosmological model, one can predict how the clustering of dark matter should evolve with time using cosmological N-body simulations. For a LambdaCDM Universe, r0 for dark matter particles is expected to increase from ~ 0.8 h-1 Mpc at z = 3 to ~ 5 h-1 Mpc at z = 0 (Weinberg et al. 2004). However, according to hierarchical structure formation theories, at high redshifts the first galaxies to form will be the first structures to collapse, which will be biased tracers of the mass. The galaxy bias is expected to be a strong function of redshift, initially >1 at high redshift and approaching unity over time. Therefore, r0 for galaxies may be a much weaker function of time than it is for dark matter, as the same galaxies are not observed as a function of redshift, and over time new galaxies form in less biased locations in the Universe.

The projected angular and three dimensional correlation functions of galaxies have been observed to z ~ 5. Star-forming Lyman break galaxies at z ~ 3-5 are found to have r0 ~ 4-6 h-1 Mpc, with a bias relative to dark matter of ~ 3-4 (Ouchi et al. 2004, Adelberger et al. 2005). Brighter Lyman break galaxies are found to cluster more strongly than fainter Lyman break galaxies. The correlation length, r0, is found to be roughly constant between z = 5 and z = 3, implying that the bias is increasing at earlier cosmic epoch. Spectroscopic galaxy surveys at z > 2 are currently limited to samples of at most a few thousand galaxies, so most clustering measurements are angular at these epochs. In one such study by Wake et al. (2011), photometric redshifts of tens of thousands of galaxies at 1 < z < 2 are used to measure the angular clustering as a function of stellar mass. They find a strong dependence of clustering amplitude on stellar mass in each of three redshift intervals in this range.

At z ~ 1 larger spectroscopic galaxy samples exist, and three dimensional two-point clustering analyses have been performed as a function of luminosity, color, stellar mass, and spectral type. The same general clustering trends with galaxy property that are observed at z ~ 0 are also seen at z ~ 1, in that galaxies that are brighter, redder, early spectral type, and/or more massive are more clustered. The clustering scale length of red galaxies is found to be ~ 5-6 h-1 Mpc while for blue galaxies it is ~ 3.5-4.5 h-1 Mpc, depending on luminosity (Meneux et al. 2006, Coil et al. 2008). At a given luminosity the observed correlation length is only ~ 15% smaller at z = 1 than z = 0, indicating that unlike for dark matter the galaxy r0 is roughly constant over time. These results are consistent with predictions from LambdaCDM simulations.

The measured values of r0 at z ~ 1 imply that are more biased at z = 1 than at z = 0. Within the DEEP2 sample, the bias measured on scales of ~ 1-10 h-1 Mpc varies from ~ 1.25-1.55, with brighter galaxy samples being more biased tracers of the dark matter (Coil et al. 2006). These results are consistent with the idea that galaxies formed early on in the most overdense regions of space, which are biased.

As in the nearby Universe, the clustering amplitude is a stronger function of color than of luminosity at z ~ 1. Additionally, the color-density relation is found to already be in place at z = 1, in that the relative bias of red to blue galaxies is as high at z = 1 as at z = 0.1 (Coil et al. 2008). This implies that the color-density relation is not due to cluster-specific physics, as most galaxies at z = 1 in field spectroscopic surveys are not in clusters. Therefore it must be physical processes at play in galaxy groups that initially set the color and morphology-density relations. Red galaxies show larger "Fingers of God" in xi(rp, pi) measurements than blue galaxies do, again showing that red galaxies at z = 1 lie preferentially in virialized, more massive overdensities compared to blue galaxies. Both red and blue galaxies show coherent infall on large scales.

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